A binomial distribution for which the number of trials n is large can well be approximated by a Poisson distribution when the probability of success, p, is:
A)larger than 0.95.
B)larger than 0.50.
C)between 0.25 and 0.50.
D)smaller than 0.05.

Question

Quizplus · Accepted Answer

When the probability of success, p, is smaller than 0.05, the conditions for a Poisson distribution approximation are met, even with a small number of trials. As the probability of success gets smaller, the variance of the binomial distribution approaches the mean, making it more similar to a Poisson distribution with the same mean. Therefore, when p is smaller than 0.05, a Poisson distribution can effectively model the situation, and the larger the number of trials, the better the approximation.

A Binomial Distribution for Which the Number of Trials N